"Another great work of this period was his 1831 paper on biquadratic residues. Here he extended some of his early discoveries in number theory with the aid of a new method, his purely algebraic approach to complex numbers. He defined these numbers as ordered pairs of real numbers with suitable definitions for the algebraic operations, and in doing so laid to rest the confusion that still surrounded the subject and prepared the way for the later algebra and geometry of n-dimensional spaces."
This quote interested me because I felt like it cemented the fact that Gauss made a lot of important papers and discoveries in his lifetime. It also amazed me that he was the one who made it possible to work with imaginary numbers, which had previously been so hard to work with. Meanwhile, I thought it was common logic, what with the numbers being represented with a variable that we use so often in equations that it just made sense to treat it as if it were a variable. I also found it interesting that such a simple idea ended up paving the way for more algebraic and geometrical discoveries, which would later affect the way we think about math today.
